چکیده (انگلیسی):

Volterra Integral Equations (VIEs) arise in many problems of real life, as, for example, feedback control theory, population dynamics and fluid dynamics. A reliable numerical simulation of these phenomena requires a careful analysis of the long time behavior of the numerical solution. Here we develop a numerical stability theory for Direct Quadrature (DQ) methods which applies to a quite general and representative class of problems. We obtain stability results under some conditions on the stepsize and, in particular cases, unconditional stability for DQ methods of whatever order.